A computationally efficient technique for fringe analysis in digital holographic interferometry using a difference equation representation of the interference field is presented. The spatially varying coefficient of the difference equation is estimated accurately by constraining it in the subspace spanned by the linearly independent basis functions. The coefficient estimated provides an accurate estimation of the interference phase derivative and enables the linear estimation of the interference field. Thereupon, the interference phase is estimated using a simple unwrapping algorithm. The performance of the proposed method is validated with the help of simulation and experimental results.